The invention relates to a storage module for interfacing with a data processing apparatus and which includes an at least partly random accessible storage device for storing digital data signals, an access device for serially accessing a series of storage locations in the storage device in order to write and read in these storage locations between a start address and a stop address, and a battery for powering the storage module when it is disconnected from the data processing apparatus. Various versions of such storage modules are known. For example, such a storage module may use an audio tape cassette. An alternative realization of such a storage module is in the form of a card, for example as a so-called chip card as described in EP-231 090. Storage modules of this kind store data signals for which it must be ensured that the storage contents are not lost when the storage module is not connected to the data processing apparatus. To achieve this, EEPROM (Electrically Erasable Programmable Read Only Memory) components are often used as a storage device for chip cards which must have a particularly flat construction. In fact, these components also retain their contents when the storage module does not receive a supply voltage; consequently, it is not necessary to include a battery in the storage module. Such EEPROM components, however, are comparatively expensive so that for many of such applications use is also made of static RAM (Random Access Memory) components which require a supply voltage in order to retain their contents but which have only a low current consumption so that the battery required in the storage module has a comparatively long service life. Even though such static RAM components are less expensive than EEPROM components, they are still comparatively expensive.